David Cameron and gangsta rap are two things you wouldn't expect to find in the same sentence, let alone the same building. But, just occasionally, truth defies expectation. The PM, it has emerged, recently played host to Dr Dre – heavyweight producer, mentor to Eminem, and one-time member of hip-hop collective Niggaz Wit Attitudes (NWA), whose hits include Straight Outta Compton and Fuck tha Police.

Well, Dave has hugged hoodies in the past, and is already known to be a musical iconoclast – the first Tory prime minister, for instance, with an affinity for the Smiths. And though Cameron has likely never been to Compton, the gritty area of LA in which NWA's famous track is set, he did join parliament from the PR firm Carlton, which technically makes him Straight Outta Carlton. Most pertinently, Dave's media adviser Craig Oliver is regularly seen draped in a pair of Beats headphones, a phenomenally successful product created and owned by Dr Dre himself. Suddenly, it all falls into place.

Or does it? Dre's visit makes things slightly prickly for George Osborne, who is said to have arranged Dre's trip to Downing Street after meeting the rapper's business partner at a do in Los Angeles. The chancellor has called tax avoidance schemes "morally repugnant". But, awkwardly, it has since emerged that part of Dre's Beats enterprise is structured in a way that allows it to reduce its UK tax bill. Oh George.

More generally, it's hard to say how many high-profile visitors check into Downing Street every year. No 10 referred me to the Cabinet Office website – which, while listing official meetings and gifts received by Cameron, does not detail the number of visitors to his residence, let alone their identities.

Nor would No 10 respond to our pressing queries about what Dre and co would have experienced on their tour of Downing Street. "It would depend on who the visitor was, and what the circumstances were," says a spokesman. But we can at least guess: presumably there would have been a five-minute hookup with Larry the mice-hunting cat, the nearest thing Downing Street has to a street-fighting gangsta. Dre might then have had a rattle round what is a surprisingly cramped space for an official residence, perhaps peeking in on the cabinet room; the office of Jeremy Heywood, the head of the civil service; and, if he was lucky, the prime minister's own second-floor flat, where we imagine the pair would have discussed Kendrick Lamar's latest and the problems created by Chris Brown's newest tattoo.